A car that weighs 14000.0 N is initially moving at a speed of 36.0 km/hr when th

Question

A car that weighs 14000.0 N is initially moving at a speed of 36.0 km/hr when the brakes are applied and the car is brought to a stop in 4.4 s. Find the magnitude of the force that stops the car, assuming it is constant. What distance does the car move during this time?

Explanation / Answer

The mass of the car (m) = W/g = 1.1 x 10^4/9.8 = 1122.45 Kg The initial velocity of car = 36 km/h = (36 x 1000)/3600 = 10 m/sec Now let the retardation produced by brakes is a m/s^2,by:- v^2 = u^2 - 2as =>0 = 10 x 10 - 2 x a x 17 =>a = 100/34 = 2.94 m/s^2 (a) Force (F) = m x a =>F = 1122.45 x 2.94 = 3300 N (b) If the initial speed is doubled i.e. = 20 m/s, now let the car stops in s meter; by:- v^2 = u^2 - 2as =>0 = 20 x 20 - 2 x 2.94 x s =>s = 400/5.88 = 68 m (c) The stopping distance in IInd case = 68/17 = 4 x stopping distance in Ist case (d) Let the time taken to stop the car in Ist case is t1 & the time taken to stop the car in IInd case is t2 sec, =>t1 = u/a & t2 = 2u/a =>t1 = 10/2.94 = 3.40 sec & t2 = 20/2.94 = 6.80 sec =>t2 = 2 x t1

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